Properties of Solids and Liquids — Easy Practice (Set 2)

Quick Recap — Fluids, Surface Tension & Heat

• Pascal's law underlies the hydraulic lift; Archimedes' principle: upthrust $= \rho_{fluid} V g$.
• Viscosity & Stokes' law: terminal velocity $\propto r^2$; continuity $A_1 v_1 = A_2 v_2$; Bernoulli $P + \tfrac12\rho v^2 + \rho g h =$ const, so faster flow means lower pressure.
• Surface tension $T$ (unit N/m): excess pressure in a drop $\dfrac{2T}{R}$, in a soap bubble $\dfrac{4T}{R}$; capillary rise $h = \dfrac{2T\cos\theta}{\rho g r}$.
• Heat: $Q = mc\Delta T$ and $Q = mL$; conduction $\dfrac{Q}{t} = \dfrac{kA\Delta T}{L}$; Stefan's law $E \propto T^4$; Newton's cooling rate $\propto \Delta T$.